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σ₀ = (1,2,3,4)(5,6)(7,8), σ₁ = (2,4,8)(3,5)(6,7), σ∞ = (2,1)(8,6,3)(5,7,4)
Base field: 1 - 2T + 6T^2 - 6T^4
Embedding: 1.094469
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